{
  "abstract": "We give a quantitative disorder comparison for the zero-field Sherrington--Kirkpatrick model at inverse temperature one. For any fixed number of replicas, replacing Gaussian couplings by independent couplings from a bounded symmetric variance-one law changes a bounded replica expectation by at most a constant times the Gaussian overlap second moment plus $N^{-1}$. A multiplicative comparison for nonnegative observables controls the tails. The proof uses Talagrand's positive-observable estimates and Yu-Ting Chen's fourth-order replica cancellation. Assuming the Gaussian critical overlap limit stated by Du and Huang, we obtain the same limit for the random quenched overlap measure in the iterated Wasserstein-2 topology. No separate moment assumption is needed for this transfer. Their additional exponential moment bound gives convergence of the rescaled spin-glass susceptibility in every finite Wasserstein distance. The coupling class includes fair signs, uniform disorder, and signs thinned at any fixed positive density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14273",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3f5fy2z63gvjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14273",
  "fulltext_url": null,
  "id": "3f5fy2z63gvjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14273",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7213274052",
  "pdf_url": "https://arxiv.org/pdf/2609.14273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3f5fy2z63gvjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14273"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Disorder transfer for the critical SK overlap law",
  "title_text": "Disorder transfer for the critical SK overlap law",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3f5fy2z63gvjz",
  "venue": "arXiv",
  "versions": []
}